SUMMARY The goal of this project is to develop novel and computationally efficient methods for analyzing bivariate alternating recurrent event data such as hospitalization data. Patients who have recurrent conditions such as psychiatric disorders or received major medical procedures such as transplant can be repeatedly admitted to hospitals. Hospitalization data usually include both admission and discharge time, which leads to an alternating sequence of in hospital stay and out of hospital periods. The two types of time periods each carry important and likely distinct information about the underlying health condition of the patients and the quality of care. Therefore, it is of interest to develop proper statistical methods that can fully utilize the rich information in hospitalization data. To our knowledge, there has been a lack of efficient statistical methods and software for analyzing such data. One can apply single-type recurrent event methods on the admission-time-only data by ignoring the discharge times. However, by using these methods one cannot distinguish whether a covariate's effect is on the length of hospital stay or the out of hospital periods, or both. For example, a new treatment that shortens in hospital stays and at the same time prolongs the out of hospital time could be deemed ineffective if it is evaluated based solely on the length between hospital admissions. In literature, there exists a nonparametric method for estimating the joint distribution of the two types of periods. However, in applications, regression methods would be more attractive. An accelerated failure time model has been proposed, but its estimation is based on a non-smooth rank-based estimating equation and its variance estimation is based on a computationally intensive resampling method. Therefore, this method has not been widely applied. In Specific Aim 1, we propose to develop a regression method which is based on a set of smooth estimating equations that are continuous and differentiable. Hence, the proposed method is expected to be more computationally stable and efficient than the existing rank-based method. In Specific Aim 2, we propose to extend an efficient resampling method for general non-smooth estimation functions to the rank-based model for more computationally efficient variance estimates. We will conduct simulation studies under various carefully designed scenarios to compare the proposed methods and existing methods. The proposed methods will also be applied to two hospitalization data, one with patients diagnosed with schizophrenia during 1981- 1995 in South Verona, Italy, and the other with adult patients (20% experiencing depression or anxiety pre- transplant) who underwent blood and marrow transplanted at the University of Minnesota during 2010-2015. An R package will be developed and made available to the public. This proposed research holds the potential to provide caregivers and policy makers the much-needed information on factors related to patients' different patterns of utilizations of health care facilities so that they can target their efforts to the populations who need improvement in their healthcare quality the most.